A band is planning to put on a concert on a Saturday afternoon. They hope to sell $15,000 worth of tickets, but they know that if it rains, they will not sell any tickets and lose $2000 for the venue rental. The week of the show, the rain forecast for Saturday is 20%.

Question

How much money should they expect to make?

Question 2 options:

$12,300

$5,200

$11,600

$9,700

Answer 1

To calculate how much money the band should expect to make from the concert, we can break it down into two scenarios: one where it rains (20% chance) and one where it does not rain (80% chance).

1. If it rains (20% probability):

   • They will sell no tickets and incur a loss of $2000 for the venue rental.
   • Expected loss: \(-2000\).

2. If it does not rain (80% probability):

   • They expect to sell $15,000 worth of tickets.
   • Expected profit (no losses): \(15000\).

Now we can calculate the expected value (or expected profit/loss):

\[ \text{Expected Profit} = (\text{Probability of rain} \times \text{Profit in case of rain}) + (\text{Probability of no rain} \times \text{Profit in case of no rain}) \]

Substituting the values:

\[ \text{Expected Profit} = (0.2 \times -2000) + (0.8 \times 15000) \] \[ = -400 + 12000 \] \[ = 11600 \]

Thus, the expected profit for the band from the concert is $11,600.

The answer is: $11,600.